Which Nikon camera lense should I purchase for portraits? And overall better photos?

I'm new photography but I'm interested in buying a new lense for my Nikon D3100. Currently I only have the 18-55mm lense that came with the camera. I would like a lense so that I can take better photos of my family and friends.
If you have any advice I would appreciate it.
I want to take advantage of any Black Friday deals that are currently happening.

Take a look at the 55-200 VR. They're about $160 or so on amazon.

An 85mm f/1.4 or a 105mm f/2 is a very good portrait lens. But it depends on your budget. Have fun.

I'd look for a nice prime lens.
the 35mm 1.8g is around $200
the 50mm 1.8g is also around $200
the 85mm 1.4g would run your over $1500
There are cheaper options like the 50mm 1.8d which runs around $115 but these 'd' lens will not auto focus with your camera. So unless you are interested in manually focusing I would suggest going with the 'g' versions.
Which one you pick really depends on what you want to shoot.
The 85mm is great for headshots but will likely be too tight for group shots or full length portraits.
The 50mm is a good portrait length on a dx camera like yours.
The 35mm is also a great lens but you might find it too wide for headshot, because it will force you to get quite close to your subject for a tight headshot.
I own both the 50mm and the 35mm. Most of the time I have the 35mm on my camera because I don't shoot a lot of headshots and I take a lot of photos inside my house of my family. I find my self taking a couple of steps back a lot with the 50mm and thats not always possible in my home so I find the 35mm more useful in those situations.
I'm sure you will be happy with any of these and you will see an improvement over you kit lens.
I'd suggest spending a day with your lens at 50mm and then a day at 35mm and see which focal length suits you best.
Or of course if you have the money to burn you can't go wrong with the Nikon 24-70mm f/2.8G and the Nikon 70-200mm f/2.8G but they will run you about $1800 and $2400 respectively.